This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
In the oil and gas industry, seismic prospecting techniques commonly are used to aid in the search for and evaluation of subterranean hydrocarbon deposits. A seismic prospecting operation consists of three separate stages: data acquisition, data processing, and data analysis and interpretation, and success of the operation depend on satisfactory completion of all three stages.
In the data acquisition stage, various methods may be used to obtain many responses from the subsurface regions. For instance, a source is used to generate an elastic signal, or wave, that propagates into the subsurface structure of the earth. The elastic wave is at least partially reflected from a boundary between one or more laminated layers, generally due to contrasts in seismic impedance between the layers. More specifically, adjacent layers in the subsurface have different lithology and physical properties and, thus, may present different densities and velocities to the elastic wave. The product of density and velocity of seismic energy transmission through each layer is called seismic impedance. The impedance contrast at the boundaries between adjacent layers causes the reflections that may then be recorded by a receiver as a seismic trace. The recorded seismic trace can be modeled as a convolution of the earth's impulse response with the seismic signal produced by the source.
During seismic survey of a subterranean region, seismic data is acquired by typically positioning the seismic source at a chosen shot location, and measuring the seismic reflections generated by the source using receivers placed at selected locations. The measured reflections are referred to as a single “shot record.” Several shot records are measured during a survey by moving the source and receivers to different location and repeating the aforementioned process. Ideally, the source and receiver locations lie on a uniformly and densely sampled grid, but this is difficult to achieve in practice for many reasons including surface obstructions, ocean currents, cable feathering, and acquisition cost. For example, the economics of seismic data acquisition may influence the spacing between receivers, e.g., lowering costs by setting the spacing as large as possible while still yielding the adequate detail in the survey results.
During the data processing stage, the recorded geophysical data (for example, seismic signals) are refined and enhanced using a variety of procedures that depend on the nature of the geologic structure being investigated and on the characteristics of the raw geophysical data. In general, the purpose of the data processing stage is to produce a data representation, such as an image, of the subsurface from the recorded data for use during the data interpretation stage. The data representation may be used to determine the general geologic structure of a subsurface region, to locate potential hydrocarbon reservoirs, and/or to guide the development of an already discovered reservoir.
The accuracy of the image obtained by the analyzing the signals may be limited by the amount of geophysical data obtained for a specific site. More specifically, the seismic data, for example, may be incomplete, providing an incomplete image to the reservoir. Although other seismic data may have been collected using different techniques or locations, combining seismic data of different types may be problematic.
Other related material may be found in the following publications: Abma, R. and Kabir, N., “3D Interpolation of Irregular Data with a POCS Algorithm” Geophysics, 71 No. 6, pp. E91-E97, (November-December 2006); Baumstein and Anderson, “Wavefield Extrapolation in Laterally Varying VTI Media”, Expanded Abstracts, SEG Annual Meeting (2003); Bauschke, H. H. and Borwein, J. M., 1996, “On Projection Algorithms for Solving Convex Feasibility Problems”, SIAM Review, 38, No. 3, pp. 367-426; Biondi, Fomel and Chemingui, “Azimuth Moveout for 3-D Prestack Imaging,” Geophysics 63, pp. 574-588 (1998); Ferguson, R, (2006), “Regularization and Datuming of Seismic Data by Weighted, Damped Least Squares”, Geophysics 71(5) pp. U67-76; Gulunay, N., “Seismic Trace Interpolation in Fourier Transform Domain”, Geophysics”, 68, No. 1 (January-February 2003), pp. 355-369; Herrmann, F. J. and Hennenfent, G., “Non-Parametric Seismic Data Recovery With Curvelet Frames”, Geophysical Journal International, 173: pp. 233-248, April 2008; Simard P. Y and Mailloux, G. E. (1990), “Vector Field Restoration by the Method of Convex Projections”, Computer Vision, Graphics, and Image Processing, 52, No. 3, pp. 360-285; and Zwartjes, P. M. and Sacchi, M. D., “Fourier Reconstruction of Nonuniformly Sampled, Aliased Seismic Data”, Geophysics, 72, No. 1 (January-February 2007). Other related material may be found in the following U.S. Pat. Nos. 5,253,193; 5,617,372; 6,307,569; and 7,202,663; and Intl. Patent App. Pub. No. WO2007/095312.